Open Access($\bar{\alpha}$, $\bar{\beta}$)-fuzzy Congruence Relation on Lattice Implication Algebras
Author(s) -
Bin Xu
Publication year - 2012
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v4n3p44
Subject(s) - overline , mathematics , congruence relation , congruence (geometry) , lattice (music) , combinatorics , bar (unit) , geometry , physics , particle physics , acoustics , meteorology
After ($alpha$, $eta$)-fuzzy congruence relation, ($overline{alpha}$, $overline{eta}$)-fuzzy congruence relation on lattice implication algebras is further investigated and it's properties is discussed, where $overline{alpha},overline{eta}in{overline{in_{h}},overline{q_{delta}},overline{in_{h}}vee overline{q_{delta}},overline{in_{h}}wedge overline{q_{delta}}}$ but $overline{alpha}eq overline{in_{h}}wedge overline{q_{delta}}$. Specially, $(overline{in_{h}},overline{in_{h}}vee overline{q_{delta}})$-fuzzy congruence relation is mainly investigate,which is generalization of $(overline{in},overline{in}vee overline{q})$-fuzzy congruence relation. Some characterizations for an ($overline{alpha}$, $overline{eta}$)-fuzzy congruence relation on $mathscr{L}$ to be a congruence and a fuzzy congruence on $mathscr{L}$ are derived